MULTISCALEMULTISCALESEGMENTATIONSEGMENTATION

Florence BFlorence BENEZIT , Jianbo SHI, 2004ENEZIT , Jianbo SHI, 2004

IntroductionIntroduction

Graph Based Object SegmentationGraph Based Object Segmentation

Wij

Wiji

j

V: graph nodesE: edges connection nodes

Image = { pixels }Pixel similarity

Segmentation = Graph partition

Pixel Affinity graphPixel Affinity graph

Normalized Cut As Generalized Eigenvalue problemNormalized Cut As Generalized Eigenvalue problem

y2i iA

y2ii

A

Program PNCX:

Relaxed to program PNCZ:

How big connection radius?How big connection radius?

BAD AND GOODBAD AND GOODEIGENVECTORSEIGENVECTORS

ACCURACY VERSUSACCURACY VERSUSCOMPUTATION TIMECOMPUTATION TIME

MULTISCALEMULTISCALEAFFINITY MATRIXAFFINITY MATRIX

AND LAYERAND LAYERCONSTRAINTSCONSTRAINTS

Long range connectionsLong range connections

Statistics of W on natural imagesStatistics of W on natural images

MultiscaleMultiscale graph decomposition graph decomposition

Multi-Multi-scalescale graph decomposition graph decomposition

Original graph weight:O(N^2)

Multi-scale graph weights:O(N)

MULTISCALE MATRIXMULTISCALE MATRIX

AVERAGE MATRIXAVERAGE MATRIX

0001/9

1/9

1/9

0000001/9

1/9

1/9

0000001/9

1/9

1/9

0

AVERAGE MATRIXAVERAGE MATRIX

Con-current partitioning of Multi-Con-current partitioning of Multi-scalescale graph graph

MULTISCALE REPRESENTATIONMULTISCALE REPRESENTATIONAND CONSTRAINTSAND CONSTRAINTS

PROBLEMPROBLEM

MAXIMIZING ENERGYMAXIMIZING ENERGY

Cross scale constraintsCross scale constraints

RELAXED PROBLEMRELAXED PROBLEM

Can be done in O(N) operations.

Computational speed upComputational speed up

RESULTSRESULTS

EXAMPLESEXAMPLES

EXAMPLESEXAMPLES

EXAMPLESEXAMPLES